This was a justified assertion at the time, given that the Physiocrats wrote before the Industrial Revolution—and in particular the widespread exploitation in manufacturing of stored solar energy in fossil fuels– and originated in France, which was then overwhelmingly a rural nation.

Smith, who was influenced by the Physiocrats and wrote in Britain when industry was starting to exploit fossil fuels (specifically coal) on a grand scale, could have corrected this oversight. But rather than following the Physiocrats’ lead on energy, Smith instead saw labour—not energy—as the font of wealth (which he described in the same terms as Cantillon: the “conveniencies of life”), and ascribed the increase in productivity over time to “the division of labour”:

The annual labour of every nation is the fund which originally supplies it with all the necessaries and conveniencies of life which it annually consumes, and which consist always either in the immediate produce of that labour, or in what is purchased with that produce from other nations…

Economics thus lost the Physiocrats’ focus on energy, and instead descended first into the “Labour theory of value” and then into the Neoclassical (and Post Keynesian) notions of “production functions” in which energy played no role at all.

The abiding weakness of all schools of economics, ever since the Classicals—including today’s Neoclassical and Post Keynesian schools, which are normally at pains to point out how superior one is to the other—is this failure to acknowledge the key role of energy in production. In this brief note, I want to record some speculations about how modern mathematically-inclined economics, with its use of production functions, might be made as energy aware as the Physiocrats were two and a half centuries ago. For the sake of non-mathematical readers, I’ve put the equations in an appendix at the end of this post.

Post Keynesian models typically see Output (Y) as a function of Capital (K) with a fixed ratio (v) between Capital and Output, and a fixed ratio (a) between Output and Labour (L) (see Equation 1).

Neoclassical economists criticise this approach because it ignores the substitutability of capital and labour in production, which they embody in their core concept of an “isoquant” which alleges that the same level of output can be produced by very different combinations of labour and capital. Post Keynesians normally respond that this substitutability is a chimera, and continue using this “fixed coefficients” model of production anyway.

Neoclassicals typically see output as a function of capital and labour where one can be smoothly substituted for the other. Their canonical model is the Cobb-Douglas Production Function with constant returns to scale (Equation 2).

Neoclassicals tout this model’s fit to empirical data as a strength; Post Keynesians note that this is simply the result of accounting identities, since this “production function” can be derived by manipulating the identity that Output equals Wages plus Profits under conditions of a relatively constant (or slowly varying) distribution of income (see Anwar Shaikh’s brilliant paper “The Humbug Production Function”).

In this “he said/she said” battle, both sides ignore the shared weakness that their models of production imply that output can be produced without using energy—or that energy can be treated as just a form of capital. Both statements are categorically false according to the Laws of Thermodynamics, which—in strong contrast to so-called “Economic Laws” like the “Law of One Price” and the “Law of Demand“—cannot be broken. As Sir Arthur Eddington once put it:

The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. (Sir Arthur Stanley Eddington, The Nature of the Physical World (1915), chapter 4)

Arguably therefore, the production functions used in economic theory—whether spouted by mainstream Neoclassical or non-orthodox Post Keynesians—deserve to “collapse in deepest humiliation”.

This unacceptable state of affairs has inspired a number of ecologically oriented economists to attempt to come up with production functions in which energy plays a crucial role. One such model is the LINEX (“LINear-Exponential”) or KLEC (“capital-labor-energy-creativity”) model used by Kummel, Lindenberger, Ayres and colleagues. At a basic level, this treats output as a function of labour, capital, energy and time—effectively adding Energy as a third input to the Cobb-Douglas model (Equation 3).

While this is an improvement on the basic Cobb-Douglas model, it still implies logically that the contribution of energy to production could be nil: just set its exponent ? to zero. This is still in violation of the Laws of Thermodynamics: we need a production function in which energy plays an essential and irreducible role.

A potential way to achieve this is to accept that the whole idea of “labour” and “capital” without energy is a farce: labour without energy is a corpse, and capital without energy is a sculpture.

Why not acknowledge this by, as an initial abstraction, treating labour and capital as both being means to harness energy to do work, and treating output (Y) itself as work? Then we start from treating Labour and Capital as means to harness the energy they contain: EL for the energy flow that a worker can harness in a day, and EK for the energy flow that a machine can harness in a day (Equation 4).

The type and amount of energy that a worker or a machine can embody (as flows of energy at a point in time) are of course vastly different: the former is limited to food, and has a biophysical maximum (say, 5000 calories per day) whereas the latter can be the Sun itself directly, agricultural products, fossil fuels, or nuclear energy, and has risen from trivial levels before the Industrial Revolution to truly astronomical levels today.

So rather than simply showing the energy embodied in labour and capital, we need to multiply it by the ratio of available energy (exergy, with ExL for labour and ExK for machinery) to energy, and by the efficiency with which that exergy is harnessed . Then, using L to signify the number of workers and K (however imperfectly) to signify the number of machines, we get Equation 5, which treats output as a function of labour, capital and energy.

Rearranging Equation 5, we can derive the basic Cobb-Douglas formulation for labour and capital, times energy inputs. This is superficially like the Kummel/Ayres LINEX formulation, but it has the advantage that the energy contribution of either labour or capital cannot be set to zero without setting the contribution of the related “factor of production” also to zero, since they have the same exponents (see Equation 6). Energy therefore plays a crucial role in production using this formulation: if the energy input is zero, then so is output.

With this term replaced by two energy related terms—one of which has a definite maximum (since there is only so much exergy that a human body can exert in a day, and this can comfortably be treated as a constant), the other of which has gone from that of a water wheel in pre-Industrial times to that harnessed by the Spacex Falcon Heavy today—the “Solow Residual” may turn out to be the exponential increase in energy and exergy input into production over time (see Figure 2).

This energy-aware model of production is just a first step in properly integrating energy and the ecological effects of using energy into economics. It does not as yet consider the different types of energy resources, the impact of energy use upon energy resources and the ecology, or the mining (not “production”) costs of energy in terms of energy itself (the “Energy Return on Energy Invested” or EROEI). But it is necessary to have a model of production in which energy plays an essential role to be able to consider these issues about the viability of our energy usage properly.

Wow! What are great concept to have an inclusive and all-encompassing approach when looking at macroeconomic situation.

In the neoliberal area of big banking and big oil, CEOs are only looking at their 10-Q-s and 10-K’s and they’re simply not considering the overall economy or the future allocation, or should I say mis-allocation, of resources and the overall impact on the economy and the environment.

America has experienced a radically regressive shift under neoliberalism and our economy in our country has morphed into a cancerous and exploitive socioeconomic business model that has become unsustainable and doesn’t consider or even address the long-term impacts or pursue workable solutions to address sustainability.

The model that the elites have chosen for a future and sustainable world is one of slavery and genocide under Agenda 21 and Agenda 2030. These globalist agendas are not a part of the national conversation and they are almost always done in secret where the people do not have a say and are purposely lied to and led astray.

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